Recent experiments reveal the long-distance cooperative and antagonistic dynamics between multiple RNAPs[1]}. The experimental evidences suggest that the superpcoil cancellation between adjacent RNAPs makes similar apparent transcription elongation rate. However, upon promoter repression or divergently transcribed genes, RNAPs switch their behavior from collaborative to antagonistic due to the build-up supercoils. There are two important dynamic behaviors that are incorporated in our two-phase model. First, RNAPs can be sensitive to the torque close to the stalling condition (5\(\sim \) 11 \(pN\)  \(nm\) )[2]}, [3]}. A static coexistence torque may not slow down or even stall the transcription elongation, but the torque fluctuation (time-dependent) may. Thus time-dependent torque may induce effects on the long-distance cooperative behaviors of RNAPs.
Second, supercoil can fast propagate as twist (torque transport) or slowly propagate as writhe (e.g, plectoneme diffusion). These two kinds of supercoiling propagations are often confounded in modeling supercoiling-dependent dynamics. During transcription elongation, the build-up supercoil can be stored in writhe and can be transmitted as twist that can be felt by RNAPs as the torsional stress[3]}, [5]}, [6]}, [2]}. The two-phase dynamic model of DNA supercoiling is expected to be applied to improve understanding the supercoiling-dependent transcription.
